derivative y=((x^3))/(3^x)

解答

导数

y = \frac{( x ^{3} )}{3 ^{x}}

\frac{x ^{2} ( 3 - ln ( 3 ) x )}{3 ^{x}}

求解步骤

\frac{d}{d x} (\frac{x ^{3}}{3 ^{x}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{3} ) 3 ^{x} - \frac{d}{d x} ( 3 ^{x} ) x ^{3}}{( 3 ^{x} ) ^{2}}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= \frac{3 x ^{2} \cdot 3 ^{x} - 3 ^{x} ln ( 3 ) x ^{3}}{( 3 ^{x} ) ^{2}}

化简

\frac{3 x ^{2} \cdot 3 ^{x} - 3 ^{x} ln ( 3 ) x ^{3}}{( 3 ^{x} ) ^{2}} : \frac{x ^{2} ( 3 - ln ( 3 ) x )}{3 ^{x}}

= \frac{x ^{2} ( 3 - ln ( 3 ) x )}{3 ^{x}}

a re a 5 x - x^{2}, y = 0

l a pl a ce t r an s f or m t^{2} - 2 t + 2

\frac{d}{d x} (e^{2 x} + x e^{2 x})

t a y l or 3 - x, 0

(2 x)^{^{'}}